Understanding of the virtual short circuit in the circuits of the operational amplifiers

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This article explains and discusses an important simplification technique used in the analysis of the operational amplifier.

A more thorough understanding of the functionality of the amplifier is, in my opinion, time well spent. These components are extremely common and rightly: are simple and versatile devices that provide the required functionality in a seemingly endless list of applications.

The analysis and design of circuits with operational is an interesting thing, for the following reason: We analyze the operational amplifiers making use of exemplary assumptions that are clearly false, But rarely we find serious problems caused by differences between the actual device and the device idealized underlying assumptions.

The virtual short

One of these assumptions is called virtual circuit, or simply virtual short. In reality, this is not one of the fundamental characteristics of an ideal operational amplifier. Rather, the virtual short is a theoretical situation that derives from one of the fundamental characteristics of an ideal operational amplifier, namely an infinite open loop gain to.

Imagine that you have an operational amplifier connected as an inverting amplifier. As almost always it happens with op amp circuits, The functionality is based on the use of feedback negativo.

the standard method to obtain an expression for the gain of this circuit is to assume that the voltage at the noninverting input terminal (VIN +) is equal to the voltage at the inverting terminal (WINE-). Since the non-inverting input terminal is grounded, VIN + = 0 V and then VIN- = 0 V. But why? Because we can assume that two different voltages are the same?

infinite Gain

We can assume that two different voltages are the same because in reality the difference between these voltages is very small and the difference between the voltages is very small because the gain is very large. Consider the following diagram:

and its equation below equation:

An operational amplifier is a differential amplifier. It produces an output voltage by applying an open-loop gain (indicated by A) the difference between the voltage at the noninverting input terminal and the voltage at the inverting input terminal. If we reorganize this equation so that the voltage difference is separated from the gain, we have the following:

Notice what happens when you increase the open loop gain (for a given VOUT): the voltage difference decreases. When the gain approaches infinity, the voltage difference approaches zero. In other words, if the gain is infinite, VIN+ It must be equal to VIN-, and this is the virtual short.

ended Gain

The inability to build an infinite gain amplifier does not nullify the practical value of the virtual short hired. Because? Because “virtual short” It is simply another way to say that there is a distinct difference between the two input voltages of the operational amplifier, and in the real circuits the difference is “close enough” a zero.

The open loop gain of the actual operational amplifiers may be greater than 100 dB. This is an output-to-input ratio of at least 100.000. Let's say if we have an operational amplifier with A = 100 dB produces an output voltage of 2,5 V we:

should read 25 μV. When the open loop gain is high enough to produce a voltage difference (very small), the virtual circuit is as reliable as a practical tool design, despite the fact that it is unrealistic.

Reflecting on the details

The Zero-Input paradox

I do not like when I am told that a gain applied to a signal 0 V produces an output to 2,5 V. I have already learned as a child that anything times zero is zero.

The ideal operational amplifier is a differential amplifier and its input signal (namely VIN +-VIN-) it is zero. Therefore, the ideal operational amplifier produces an output voltage equal to zero in all conditions … considered from this point of view does not seem a very useful device.

Naturally, this is the point where the hypothesis proves partially unfounded. You can not use the virtual circuit to determine VOUT according to the normal function of open loop of the operational amplifier. Rather, the virtual short is a tool that is used when the operational amplifier is implemented in the context of negative feedback.

Eg, When we are analyzing a non-standard inverting amplifier, the virtual short hypothesis (in conjunction with the assumption of zero input current) It allows us to derive an expression for the closed-loop gain as if the op amp was not even there.

When I look at this circuit, my mind naturally ignores the triangle depicting the operational, the triangle is like a stone thrown in the water flow of a river. The current flows around it without increments and subtraction of the total current flowing.

The input is an input or an output?

If you put on the ground the inverting input terminal of an operational amplifier and applies a signal from 1 V to the non-inverting input terminal, the output will saturate and will move close to the positive supply and the difference between VIN + e WINE- Sara 1 V. There is nothing surprising in this speech; the high open-loop gain of the pilot device the output at the maximum output voltage and the input voltage remains at 1 V.

However, when we start to talk about the Virtual Short, The situation is less clear. It almost seems that the operational amplifier is using its high gain to force the equal sign of the input voltages. In the inverting configuration, eg, one input is grounded and the other receives the input signal, but then the operational amplifier decides that those two voltages must be equal. What it is really happening?

Again, the virtual short-circuit hypothesis is something that exists in the context of a negative feedback amplifier. In the inverting configuration, the inverting input terminal is connected not only to the input signal (through a resistor) but also to the output terminal (through a resistor). The output voltage affects the voltage at the inverting input terminal, and the operational amplifier gain affects the output voltage, and this leads to my final statements about what is actually the virtual circuit:

  • The presence of a negative feedback network establishes a relationship output-to-input;
  • the difference between VIN + e WINE- It must be consistent with the gain imposed by the closed-loop feedback network;
  • then, the circuit naturally creates a situation where the difference between the inverting and non-inverting input voltage is very small, because the only way to produce a typical output voltage from an amplifier at extremely high gain difference is to have a very small voltage difference .

Conclusion

I hope that this discussion has served to better understand the virtual circuit supposition.

Amilcare

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